I have to solve a transcendental equation for a parameter, say $\beta$. Now, the $\beta$ has a range from $ik$ to $k$ where $i$ is the usual imaginary root $\sqrt{-1}$ and $k$ is a real number. Problem is, the transcendental equation has multiple solutions, and so I cannot guess what will be the proper choice for the initial value of $\beta$ in FindRoot. I could do it if $\beta$ ranges from $p$ to $q$ where $p$ and $q$ are reals by plotting the transcendental equation's lhs and rhs. However, I don't know how to plot complex ranges.
Is there any way to guess the initial values?

say the equation is x=y where x and y contains bessel functions and its derivatives. I have to solve it for beta. If beta ranges from p to q where p and q are real numbers. I could write Plot[{x,y},{beta,p,q}] Then from the plot i get a feel for good values. But i*k to k (where i is the usual imaginary root sqrt(-1) and k is a real number) is the allowed range for beta and i cannot write Plot[{x,y},{beta,i*k,k}] it surely gives me error! By using FindRoot[x==y,{beta,_initial value_}] I get solution though but changing initial value just a little beta changes completely.
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4208Apr 10 '13 at 22:20

One option is manual: right-click on the image, click "Get Coordinates", pick out and click on a crossing, and then press Ctrl+C to copy the coordinates. For instance, if I want the root of least magnitude, my attempt at performing that procedure yields the point {1.453, 1.887}, which can then be fed to FindRoot[]:

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